Foundation June 2024 Paper 2 Q26
26 Solve the simultaneous equations
\[\begin{aligned} 6x + 4y &= 1 \\ 3x + 5y &= 8 \end{aligned}\]Show clear algebraic working.
(3)
| Scheme | Marks |
|---|---|
eg \(\begin{aligned} 6x + 4y &= 1 \\ -\ \ 6x + 10y &= 16 \\ (6y &= 15) \end{aligned}\) or \(\begin{aligned} 30x + 20y &= 5 \\ -\ \ 12x + 20y &= 32 \\ (18x &= -27) \end{aligned}\) oe or eg \(6x + 4\left(\dfrac{8 - 3x}{5}\right) = 1\) or \(3\left(\dfrac{1 - 4y}{6}\right) + 5y = 8\) | M1 |
| M1dep | |
| working required Answer: \(x = -1.5\), \(y = 2.5\) | A1oe |
| (3) | |
| (3 marks) |
Notes
M1: A correct method to eliminate \(x\) or \(y\) – multiplying one or both equations so that one value can be eliminated and the correct operation to eliminate which can be shown by 2 out of 3 terms correct for subtraction or addition
(allow one arithmetic error in multiplying)
or
for a correct substitution of one variable into the other equation.
NB: the mark is for the method and not for the result of the method – although if the correct result is seen, this means the mark is awarded
M1dep: A correct method to calculate the value of the other letter (dep on M1) eg substitution of found variable into an equation (equation does not need to be solved) or starting again with elimination or substitution